Hadamard introduced the concept of finite parts of divergent integrals.i.e.Hadamardprincipal value,when he researched the Cauehy problems of the hyperbolic type partialdifferential equations.In this paper,the authors try to generalize this concept to the singularintegrals on a sphere of several complex variables space C~n.The Hadamard principal valueof higher order singular integralis defined and the corresponding Plemelj formula is obtained.